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Select the outlier in the data set.\newline32,36,38,39,40,42,43,45,92132, 36, 38, 39, 40, 42, 43, 45, 921\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease

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Q. Select the outlier in the data set.\newline32,36,38,39,40,42,43,45,92132, 36, 38, 39, 40, 42, 43, 45, 921\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease
  1. Identify Outlier: Identify the outlier in the given data set.\newlineThe data set is: 32,36,38,39,40,42,43,45,92132, 36, 38, 39, 40, 42, 43, 45, 921.\newlineAn outlier is a value that is significantly higher or lower than the rest of the data. In this case, 921921 is much higher than all other values, so it is the outlier.
  2. Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included.\newlineMean = (32+36+38+39+40+42+43+45+921)/9(32 + 36 + 38 + 39 + 40 + 42 + 43 + 45 + 921) / 9\newlineMean = (1236+921)/9(1236 + 921) / 9\newlineMean = 2157/92157 / 9\newlineMean ≈239.67\approx 239.67
  3. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier.\newlineMean without outlier = (32+36+38+39+40+42+43+45)/8(32 + 36 + 38 + 39 + 40 + 42 + 43 + 45) / 8\newlineMean without outlier = 315/8315 / 8\newlineMean without outlier ≈39.375\approx 39.375
  4. Compare Mean Changes: Compare the means to determine if the mean would increase or decrease upon the removal of the outlier. The mean with the outlier is approximately 239.67239.67, and the mean without the outlier is approximately 39.37539.375. Removing the outlier significantly decreases the mean.

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